Geodesically completing regular black holes by the Simpson-Visser method

TL;DR

This paper introduces a method to transform geodesically incomplete regular black hole solutions into complete, symmetric solutions using the Simpson-Visser regularization, enabling the construction of wormholes or black holes with novel horizon structures.

Contribution

The authors adapt the Simpson-Visser method to regular black holes, creating geodesically complete, symmetric solutions applicable to various spherically symmetric spacetimes.

Findings

Constructed a geodesically complete regular black hole solution.

Demonstrated the solution can be a wormhole or black hole with different horizon configurations.

Derived a source Lagrangian involving phantom scalar and nonlinear electromagnetic fields.

Abstract

Regular black holes are often geodesically incomplete when their extensions to negative values of the radial coordinate are considered. Here, we propose to use the Simpson-Visser method of regularising a singular spacetime, and apply it to a regular solution that is geodesically incomplete, to construct a geodesically complete regular solution. Our method is generic, and can be used to cure geodesic incompleteness in any spherically symmetric static regular solution, so that the resulting solution is symmetric in the radial coordinate. As an example, we illustrate this procedure using a regular black hole solution with an asymptotic Minkowski core. We study the structure of the resulting metric, and show that it can represent a wormhole or a regular black hole with a single or double horizon per side of the throat. Further, we construct a source Lagrangian for which the geodesically complete spacetime is an exact solution of the Einstein equations, and show that this consists of a phantom scalar field and a nonlinear electromagnetic field. Finally, gravitational lensing properties of the geodesically complete spacetime are briefly studied.